[AndrewC]

Of course, from this fundamental “not” gate, as computer scientists call it, all digital logic follows.

What!!? '~' alone is not sufficient to generate all truth tables. 'nor' or 'nand' are sufficient.

[Doctor Stochastic]

Speaking of Bertrand Russell, why did he and G.E. Moore choose Not and And for their reduced forms? Your Nand and Nor would have been more "economical" in terms of operators. (The CRAY-1 used only a 5-4 Nand gate for logic; plus memory and register chips. Three types of chips, off the shelf.) Modern books prefer And, Or, Not, Implies, and Equivalent, because these seem to be easier to read. Principia Mathematics is hard to read more because of the choice of notation that because of the difficulty of its proofs.